We study the dynamics of bubbles in the one dimensional Cahn-Hilliard equation. For a gas of diluted bubbles we find ordinary differential equations describing their interaction which permits us to describe the ulterior dynamics of the system in very good agreement with numerical simulations.

Abstract. -Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics.Introduction. -In this letter we focus our attention on a growth model that was first used to describe the statistical behavior of a population of individual species; for example, human population growth. This is an area of interest several centuries old and is perhaps one of the oldest branches of biology to be studied quantitatively. The first model for human population growth was proposed by Malthus in 1798. In 1838 Verhulst [1] corrected this first model taking into account both the limitation of the growth of a population due to the competition between individuals, and the limitation on the density of the population that the environment can support. An example of this would be the limitation on the amount of food that the system is capable of producing. The proposed equation is known as the logistic equation,ẋ = a 0 x(1 − x).There are many examples of assemblies that consist of a number of elements that interact through cooperative or competitive mechanisms. Some important examples include species that share a given environment, such as animals that live in the seas and rivers of our planet; the components of the central nervous system of a living being; transmission of diseases caused by different types of viruses; interacting vortices in a turbulent fluid; coupled

We report an exact result for the calculation of the probability distribution of the Bernoulli-Malthus-Verhulst model driven by a multiplicative colored noise. We study the conditions under which the probability distribution of the Malthus-Verhulst model can exhibit a transition from a unimodal to a bimodal distribution depending on the value of a critical parameter. Also we show that the mean value of x(t) in the latter model always approaches asymptotically the value 1.

A revision of generalized commutation relations is performed, besides a description of Non linear momenta realization included in some DSR theories. It is shown that these propositions are closely related, specially we focus on Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized commutators. Due to this, a new algebra arises with its own features that is also analyzed.

Multistable systems can exhibit stochastic resonance which is characterized by the amplification of small periodic signals by additive noise. Here we consider a nonmultistable linear system with a multiplicative noise forced by an external periodic signal. The noise is the sum of a colored noise of mean value zero and a noise with a definite sign. We show that the system exhibits stochastic resonance through the numerical study of an exact analytical expression for the mean value obtained by functional integral techniques. This is proof of the effect for a very general kind of noise which can even have a definite sign.